Solve for $c$. $12c-4=14c-10$ $c=$
Solution: We need to manipulate the equation to get $ c $ by itself. $\begin{aligned} 12c-4&=14c-10 \\\\ 12c-4 {-14c} &= 14c-10{-14c} &&\gray{\text{Subtract 14c from each side.}}\\\\ -2c-4&=-10 &&\gray{\text{Combine like terms.}}\\\\ -2c-4{+4} &= -10{+4} &&\gray{\text{Add 4 to each side.}}\\\\ -2c &=-6 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-2c}{{-2}} &= \dfrac{-6}{{-2}} &&\gray{\text{Divide each side by -2.}}\\\\ c &= {3} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $ c= { 3 }~~~~~~~~$ [Let's check our work!]